Question:
What is the result of substituting for y in the bottom equation? y = x – 3 y = x2 + 2x – 4 A. (x – 3) = x2 B. y = (x – 3)2 + 2(x – 3) – 4 C. x – 3 = x2 + 2x – 4 D. y = x2 + 2x – 4 – (x – 3)
Answer:
Option C: [tex]x-3=x^{2}+2 x-4[/tex] is the resulting equation
Explanation:
Given that [tex]y=x+3[/tex] and [tex]y=x^{2}+2 x-4[/tex]
We need to determine the resulting equation by substituting the value of y in the equation [tex]y=x^{2}+2 x-4[/tex]
Option A: [tex]x-3=x^{2}[/tex]
Substituting the value of y in the second equation does not results the equation [tex]x-3=x^{2}[/tex] because the last two terms [tex]2x-4[/tex] is missing.
Hence, Option A is not the correct answer.
Option B: [tex]y=(x-3)^{2}+2(x-3)-4[/tex]
This is not the resulting expression because instead of substituting the value for y, it has been wrongly substituted for x.
Hence, Option B is not the correct answer.
Option C: [tex]x-3=x^{2}+2 x-4[/tex]
This is the resulting expression because substituting [tex]y=x+3[/tex] in the second equation, we get, [tex]x-3=x^{2}+2 x-4[/tex]
Hence, Option C is the correct answer.
Option D: [tex]y=x^{2}+2 x-4-(x-3)[/tex]
This is not the resulting expression because instead of substituting the values for y, the value of y has been subtracted.
Hence, Option D is not the correct answer.
